How I can disprove this $-x\neq x \implies x^2\neq x^2$ with $x$ is a positive real number?

Question

let $x$ be a positive real number , Really am not familiar with mathematical logic as well ? I came accrosse this proposition :$-x\neq x \implies x^2\neq x^2$ in my mind which i can't disprove it , Any idea ?

Answer 1

Easy: Take any positive $x$. Then $-x \not = x$, but $x^2 = x^2$. So, the antecedent is true, and the consequent false, and hence the statement is indeed false.

In fact, for a counterexample, you can just take any specific $x$, say $x=1$. Again, we have $-1 \not = 1$, but $1^2 = 1^2$. So, $x=1$ is a counterexample to the claim that $-x\neq x \implies x^2\neq x^2$ for any positive real number $x$